coupons can be reinvested

[BrainMan]

Here's a question from a CAS Exam 2. Can someone show me how to do it. I know the answer is (A), but I'm not sure why.

A 30-year bond has 10% annual coupons and a par value of 1000. Coupons can be reinvested at a nominal annual rate of 6% convertible semi-annually. X is the highest price that an investor can pay for the bond and obtain an effective yield of at least 10%

Calculate X.

(A) 518

(B) 618

(C) 718

(D) 818

(E) 918

Thanks in advance for your help.

[lee_onion]

Here's a question from a CAS Exam 2. Can someone show me how to do it. I know the answer is (A), but I'm not sure why.

A 30-year bond has 10% annual coupons and a par value of 1000. Coupons can be reinvested at a nominal annual rate of 6% convertible semi-annually. X is the highest price that an investor can pay for the bond and obtain an effective yield of at least 10%

Calculate X.

(A) 518

(B) 618

(C) 718

(D) 818

(E) 918

Thanks in advance for your help.

Here's my solution:

X=(100*s(30|i) + 1000) * 1.1^(-30) = 517.62, which s(n|i) is the accumulation value of the annuity at the effective rate i for n years and i = 1.03^2 - 1